Note that slowly resp. regularly varying functions include functions which are
neither
increasing nor decreasing. By [1]} it follows that
any function \(\ell \)  that
varies regularly with index \(\rho \in {\mathbb {R}}\)  is of the form
\(\ell (r)=r^{\rho }\ell _0(r)\)  for some
function \(\ell _0\)  that varies slowly.
